Domain is a term used to describe a variable for which a set of functions or signals are defined.
Time-domain describes functions or signals that change over time; depth-domain describes functions or signal that change over space. The oscillioscope, geophone, and heartrate monitor are tools used to visualize real-world signals in the time domain. The map, photograph, and well log are tools to describe signals in the depth (spatial) domain.
Because seismic waves are recorded in time (jargon: time series), seismic data are naturally presented and interpreted with time as the z-axis. Routinely though, geoscientists must convert data and data objects between the time and depth domain.
Consider the top of a hydrocarbon-bearing reservoir in the time domain (top panel). In this domain, it looks like wells A and B will hit the reservoir at the same elevation and encounter the same amount of pay.
In this example the velocities that enable domain conversion vary from left to right, thereby changing the position of this structure in depth. The velocity model (second panel) linearly decreases from 4000 m/s on the left, to 3500 m/s on the right; this equates to a 12.5% variation in the average velocities in the overburden above the reservoir.
This velocity gradient yields a depth image that is significantly different than the time domain representation. The symmetric time structure bump has been rotated and the spill point shifted from the left side to the right. More importantly, the amount of reservoir underneath the trap has been drastically reduced.
Have you encountered examples in your work where data domains have been misleading?
Although it is perhaps more intuitive to work with depth-domain data wherever possible, sometimes there are good reasons to work with time. Excessive velocity uncertainty makes depth conversion so ambiguous that you are better off in time-domain. Time-domain signals are recorded at regular sample rates, which is better for signal processing and seismic attributes. Additionally, travel-time itself is an attribute in that it may be recorded or mapped for its physical meaning in some cases, for example time-lapse seismic.
If you think about it, all three of these models are in fact different representations of the same earth. It might be tempting to regard the depth picture as 'reality' but if it's your only perspective, you're kidding yourself.